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AIR FORCE REPORT NO. SAMSO-TR-7 3-136

AEROSPACE REPORT NO. TR-0073 (3450-16) -2

A73 01458

Cl

_,

5026242

Predicted Radar Cross Section of Thin,

Long Wires Compared with Experimental Data

Prepared by J. RENAU and M. T. TAVIS

Electronics and Optics Division Engineering Science Operations

72 OCT ~~

Reentry Systems Division

THE AEROSPACE CORPORATION

Prepared for SPACE AND MISSILE SYSTEMS ORGANIZATION

AIR FORCE SYSTEMS COMMAND LOS ANGELES AIR FORCE STATION

Los Angeles, California

APPROVED FOR PUBLIC RELEASE: DISTRIBUTIONRmJJiNE~Q UBRA~Y.

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~-~ir Force Report No. o J.-.!2. AMS 0- T R- 7 3 - 1 3 6

Aerospace Report No. I [j_R-0073(3450-16)-2

PREDICTED RADAR CROSS SECTION ·oF THIN, LONG WIRES

COMPARED WITH EXPERlMENTAL DATA.·.

Prepared by

J. Renau and' M. T. Tavis ·

Radar and Power Sub,division Electronics and Optics Division Engineering Science Operations

72 OCT 01

~;;_ntry Systems Division THE ~ROSPACE CORPORATION . . i El Seg~ndo, California

Prepared for

SPA~~:\~D MISSILE SYSTEMS ORGANIZATION ------"' ~ FORCE SYST;EMS COMMAND

LOS ANGELES AIR FORCE STATION Los Angeles, California

Approved for public relea$e; distribution unlimited

FOREWORD

This report is published_ by The Ae.rospace Corporation, El Segundo,

California, under Air Fore~ c.ontra~t No. F04701-72-C-0073. This report

was prepared by the Electronics and Optics Division, Engineering Science

Operations, at the request of Concepts and Plans Group, Reentry Systems

Division.

This report, which documents research carried out from December 1971

through September 1972, was submitted for review and approval on

31 January 1973 to Ronald L.' Adams, 2nd Lt, USAF, SAMSO (RSSG).

The authors acknowledge with gratitude the assistance of Mary Barling,

John Kohlenberger and Dr. William Helliwell who aided in preparing the

computer-generated figures used in this study. The authors also thank

Dr. Duclos for his backing of the study.

• W. Capps, Director Radar and Power Subdivision Electronics and Optics Division Engineering Science Operations

. ·'

Approved by

G. R. Schneiter, Director Program Definition

· Concepts and Plans Reentry Systems Division :be'velopment Operations

Publication of this report does not constitute Air Force approval of

the report's findings or conclusions. It is published only for the exchange

and stimulation of ideas.

ii

~~ · 6Rona:idL Adams, 2nd Lt, USAF ECM/Pen Aids Project Officer System Engineering Directorate Deputy for Reentry Systems

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ABSTRACT

In order to determine the validity and accuracy of Radar Cross

Section (RCS) predictions for thin wires, the predictions of the closed-form

expressions developed by Chu, Tai, Van Vleck, et al., and Ufimtsev have·

been compared with carefully measured backscattered RCS vs angle of

incidence for various length thin, long, cylindrical conductors. Further,

the prediction of an open-form numerical analysis based on the Source

Distribution Technique and programmed by M. B. Associates as the BRACT

computer program was also compared with the experimental data.

It was found that ( 1) the BRACT computer results agree with experiment --- --~~-------··- -- ·-

so well (within ±1 dB for all reliable data) that it may be used with great con-

fidence for any length thin wires and can be used as reference data for com­

paring with the predictions of the closed-form solutions; (2) the results of

Chu are not accurate except at broadside incidence; (3) the results of Tai

compare favorably with data up to k.e values of about 17 if corrections are

made to the approximate formulas to correct for broadside incidence; (4) the

results of Ufimtsev compare well with experiment for all kt values considered;

and (5) the results of Van Vleck, et al., appear to be very accurate for all k1

values considered except for near end-on incidence. In a separate report to

be published soon one of the authors of this report (M. Tavis) has shown that

this deficiency is due to numerical approximations in the theoretical

expressions.

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CONTENTS

ABSTRACT ......... .

I.

II.

III.

IV.

A.

B.

c. D.

INTRODUCTION

WIRE DIMENSIONS AND RCS DATA

THEORET~ALEXPRES@ONSANDTHESDT

COMPUTER PROGRAM .......•.......

A Review of Tai's Theoretical Expressions and Comparison of Predictions with Data ....... .

Predictions Based on Van Vleck's, et al., Expression and Comparison with Data . . . .•...

Ufimtsev' s Solution

SDI Technique

CONCLUSIONS

REFERENCES

APPENDIX A .

v

iii

l

3

5

7

10

12

15

17

19

A-1

l.

2.

3.

I

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

FIGURES

Measured Backscattered RCS for Thin, Metallic Straight Wires, kQ = 4. 44, Circular Polarization

Measured Backscattered RCS for Thin, Metallic Straight Wires, ki! = 9. 2, Circular Polarization

Measured Backscattered RCS for Thin, Metallic Straight Wires, kQ = 11. 7, Linear Polarization

Measured Backscattered RCS for Thin, Metallic Straight Wires, kQ = 13, Circular Polarization

Measured Backscattered RCS for Thin, Metallic Straight Wires, kQ = 17, Linear Polarization ..

Measured Backscattered RCS for Thin, Metallic Straight Wires, kQ = 34. 8, Linear Polarization.

Measured Backscattered RCS for Thin, Metallic Straight Wires, kQ = 45.7 .. , ........... .

Comparison of Tai' s Predicted RCS with Measured Data, kQ = 11.7 .........••............

Comparison of Chu' s Predicted RCS with Measured Data, kQ = 11.7 ...................... .

Comparison of Tai' s Predicted RCS with Measured Data, kQ = 4~44 ...............•........

Comparison of Chu' s Predicted RCS with Measured Data, kQ = 4. 44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Comparison of Modified Tai' s Prediction with Measured RCS Data, kQ = 11.7 ........................ .

Comparison of Modified Tai' s Prediction with Measured RCS Data, ki! = 13 ........•..•.••..........

Comparison of Modified Tai' s Prediction with Measured RCS Data, ki! = 9. 2 ...........•.•...........

vi

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.

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21

22 ·I 23 I 24 I 25

26

27 I 28

I 29

I . . . . 30

I . . . . 31

. . . . 32

. . . . 33

. . . . 34

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I FIGURES (cont. )

~

t 15. Comparison of Modified Tai' s Prediction with Measured

RCS Data, kP = 4. 44 .............•........... 35

l, 16. Comparison of Modified Tai' s Prediction with Measured RCS Data, kR = 17 .......•..••.........••.. 36

I 17. Comparison of Modified Tai' s Prediction with Measured

RCS Data,· kQ = 45. 7 ........................ . 37

18. Comparison of Van Vleck's Predicted RCS with Measured

I Data, k2 = 4. 44 . ............................ • 38

19. Comparison of Van Vleck's Predicted RCS with Measured

I 20.

Data, k2 = 9. 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Comparison of Van Vleck's Predicted RCS with Measured

I 21.

Data, k£ = 11.7 ............................ . 40

Comparison of Van Vleck's Predicted RCS with Measured Data, k2 = 13 ............................ . 41

I 22. Comparison of Van Vleck's Predicted RCS with Measured Data , k£ = 1 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

I 23. Comparison of Van Vleck's Predicted RCS with Measured Data, kQ =45. 2 ........•.................... 43

I 24. Comparison of Ufimtsev' s Predicted RCS with Measured Data, kQ = 4. 44 ................•.........•. 44

I 25. Comparison of Ufimtsev' s Predicted RCS with Measured Data, kQ = 9. 2 . . . . • . . . . . . . . . . . . . . . . . . . . • . . 45

I 26. Comparison of Ufimtsev's Predicted RCS with Measured

Data, kQ = 11.7 ......••................... 46

2 7.

I Comparison of Ufimtsev' s Predicted RCS. with Measured Data, k2 = I 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

28. Comparison of Ufimtsev' s Predicted RCS with Measured

I Data, k2 = 1 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

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I

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

1.

FIGURES (cont. )

Comparison of Ufimtsev' s Predicted RCS with Measured Data, kQ = 45. 7 ........................... .

Comparison of BRACT Calculated RCS with Measured Data, k Q = 4. 44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Comparison of BRACT Calculated RCS with Measured Data , ki = 9 . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . ~

Comparison of BRACT Calculated RCS with Measured Data, k Q = 1 1 • 7 • • • • • • • • • . • • • • • • • • • • • • • • • •

Comparison of BRACT Calculated RCS with Measured Data, kQ = 1 3 . • • . • . • • • • ; • • • • • • • • • . • . . • •

Comparison of BRACT Calculated RCS with Measured Data, kQ = 1 7 . . • • • • • • • • . • • • . • • . • • • • • • • • •

Comparison of BRACT Calculated RCS with Measured Data, kQ = 34. 8 ......................... .

Comparison of BRACT Calculated RCS with Measured Data, kQ = 45. 7 . . . . . . . ....

BRACT Calculated RCS, kQ = 157

Van Vleck vs 1.Himtsev Predicted RCS Values, k£=157 .....•......•..........•..

Comparison of the Generalized Van Vleck Formulation with Van Vleck's original Expression, k1 = 13 ••.•••.•.•..

TABLE

Experiment Parameters .......................... .

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50

51

52

53

54

55

56

57

59

61

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I. INTRODUCTION

Interest in the backscattered Radar Cross Section (RCS) of thin,

long, cylindrical conductors has led several organizations including The

Aerospace Corporation to obtain RCS measurements vs angle of incidence

for various length thin, long, conducting wires.

Having assembled such carefully measured RCS data, it was logical to

use the more commonly known closed-form theoretical expressions published

in the literature on this subject for comparison purposes. The relatively

simple analytical expressions used are those derived by Chu (unpublished

but discussed by Van Vleck, et al., in Ref. 1, and used in Ref. 2), by

Van Vleck, et al. (Ref. 1), and Tai (Ref. 3),':' and the known expressions

derived by Ufimtsev in relatively recent publications (Refs. 4 and 5).

The purpose of this technical report is twofold. The first purpose is

to compare the predictions from the four theoretical expressions with the data

over a wide range of length-to-wavelength ratios in order to establish which

theoretical expression possesses general validity for predicting all the experi­

mental data considered and to within what accuracy. The second purpose

is to compare with the data the RCS predictions obtained by using a computer

program specifically designed to yield the RCS of thin, not necessarily

straight, conducting wires.

* Equations (21) and (22) given by Tai are expressions averaged over the polarization angle. In order to recover the expression before the averaging process, multiply Eqs. (21) and (22) of Tai by 8/3 cos44J. Moreover, there is a misplaced bracket in the logarithmic term of these equations. For this reason, the corrected forms will be given in the text of this report.

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II. WIRE DIMENSIONS AND RCS DATA

In May 19 68, an RCS experiment on thin wire configurations was

conducted at the Radar Target Scatter (RATSCAT) Division at Holloman Air

Force Base, New Mexico. This experiment was directed by J. W. Curtis

and L. Martinez of The Aerospace Corporation. A thin, straight wire was

one of the configurations measured under this effort. The radar frequency

chosen for the straight wire experiment was 450 MHz (radar wave­

length X. = 2/3 m). Because of practi~al limitations, yet desiring to

achieve a large value of kQ (where kQ = 2rr Q I A and 2Q = L = total length of

wire), a copper wire with a total length of 2.48 mwas chosen, i.e., kQ = ll. 7.

The radius of the wire was "a" = 4 X 10- 4 m ( 15. 8 mil) or ka = 2rra/ A = 3. 78

X 10-3

• The linearly polarized electric field vector of the radar was chosen - -in the plane formed by k and J. so that cos ljJ = 1. The wire located in the far

field of the radar was mounted on a very low RCS support (styrofoam holder)

such that -40 dbsm cross section could be measured with a signal-to-noise

ratio of about iO dB. The calibration measurements performed on known

size spheres were accurate to within 1 dB of the predicted RCS. During the

RCS vs angle measurement, the angular accuracy was about± 1 deg.

Subsequently, the measured RCS values of more pieces of differing length

wires became available, and the seven almost randomly selected data for

presentation in this report are a good representation of reliable RCS

measurements over a wide range of kQ values, where the radius "a" of each

wire is such that ka << l.

The measured backscattered RCS data in decibels relative to a meter

square (dbsm) vs aspect angle (90 deg at broadside) for the differing length,

thin, metallic straight wires are shown in Figs. 1 through 7. * The accuracy

of the RCS measurements is within about 3 dB at the peaks and degrades at the

.),

"'In Fig. 7, the angle 8 is zero at broadside and 90 deg at grazing incidence.

3

nulls of the RCS patterns based on calibrating spheres. The errors in the

Avco data (Fig. 6) are larger. The angular accuracy is about ±l deg. The

pertinent parameters of each experiment are given in Table l.

Fig. No.

l

2

3

4

5

6

7

Table l. Experiment Parameters

Source of Data

Lincoln Lab. (Ref. 6), per­formed by Sigma Inc. , Fla.

Lincoln Lab (Ref. 6)

SAMSO/ Aerospace Corp., per­formed at RATSCAT

Lincoln Labb (Ref. 6)

Univ. Michigan

Avcoc

M. B. Associ­ates, per­formed at Sigma Inc., Fla.

Wavelength, m

0.227

0.227

0.666

0.227

Set at l. 00

0.69

Set at l. 00

Polarization a Transmit Receive· ka

Circular Circular 4. 2 X 10-3

4. 44

Circular Circular 4. 2 X 10-3

9. 2

Linear Linear. '3. 7 8 X lO- 3 ll. 7

Circular Circular 4.2Xl0- 3 13

Linear Linear 3.95Xl0- 2 17

Linear Linear 9. l X 10- 3 34.8

Linear Linear 0.22 45.7

aCircular Transmit and Receive RCS will be 6 dB below that of Linear Transmit and Receive.

bLincoln Labs data appears to be somewhat in error up to the first null.

· c Avco data is several decibels in error due to experimental difficulties.

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III. THEORETICAL EXPRESSIONS AND THE SDT COMPUTER PROGRAM

Tai's expression(Ref. 3, Eq. 21) for the backscattered RCS from long

thin wires with k.t » 1 and ka << 1 when the wire is nonresonant (namely k 1 is nrr

not equal to Z' n = 1, 2, 3, •.• ) is

X 1

[l / co;29

sin(2kicos9) . 4a cos s1n

- l - cos(2kQ )cos(2kQcos e)] 2

sin2ke ( 1)

The expression derived by Chu (unpublished) for the same conditions and

. referenced by Van Vleck, et al. (Ref. 1), also given in Ref. 2, is

(2)

where

o- = radar cross section

a = radius of wire

2R = total length of wire

Qnx = natural logarithm of x

RnY = 0.5772 orY::::: 1.78

k .2rr = A

5

e = aspect angle ( e = 90 deg at broadside incidence)

l\J = polarization angle, defined as the acute angle between_!he _ incident electric field vector and the plane defined by k and £

P(l\J) = cos 4

l)J for the case of transmitted linearly polarized waves and received in the same direction; for random polarization,

2rr

p = 2~ J cos 4

l\Jdl\J =~. 0

2 P( .l') COS l\J t • 1" • • h 1 f • 1 't' = 2 ransm1t 1near, rece1ve r1g tor e t cucu ar

P(l\J) = ! transmit right or left circular, receive right or left circular

To test the validity of the theoretical expressions for thin, long wires

of infinite conductivity, the parameters of the copper wire used at the RA TSCAT

Center were inserted in the expressions Eqs. (1) and (2), with P(l)J) = 1, and the

predicted eros s sections a:( 9) vs e were obtained. The predictions from

Tai 1 s expression are plotted in Fig. 8, where the experimental data are also

shown for comparison. The predictions obtained from Chu' s expression,

together with the same data, are plotted in Fig. 9. In both figures, the ordinate

is the absolute backscattered eros s section in dbsm vs the aspect angle with

respect to the wire.

The results of Figs. 8 and 9 indicate that for kl = 11.7, Tai 1s expression

predicts the correct number of lobes in the RCS vs angle pattern and, within

a few decibels and degrees in position, the magnitude of the predicted RCS

agrees with the data except near the nulls. Chu 1 s expression yields results

that agree very well with the data only near broadside (aspect angle near

90 de g), but leads to very erroneous results at all other angles. Chu 1 s

expression for all the other wires discussed in this report led to similar

erroneous results, except at broadside incidence.

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A further test of Tai 1 s and Chu 1 s expressions is obtained by using the

parameters of Fig. 1 and Table 1. The predicted values from Tai's

expression are shown in Fig. 10 and those of Chu' sin Fig. 11. In both

figures, the data have also been plotted for comparison purposes. It is clear

that Chu' s expression for broadside is the more accurate one .

A comparisonofEqs. (l)and (2)for the aspect angle 8 = 90deg reveals

that Tai' s expression at broadside reduces to:

1 p ( lJJ)

7T ~;t + [ en(Y~a)J 2

and Chu' s expression reduces to:

P(l);)

(kQ _ 1 ~ cos2kQ)

2

sm2kQ (3)

(4)

Equations (3) and (4) at 8 = 9 0 deg are identical except for the second

term in brackets in Tai's expression. Indeed, it will be shown below that the

correct asymptotic (ki » 1) equation that one obtains from Tai 1 s expression at

8 = 90 deg, i.e., broadside, is Eq. (4) and not Eq. (3) as published.

A. A REVIEW OF TAl'S THEORETICAL EXPRESSIONS AND COMPARISON OF PREDICTIONS WITH DATA

According to Ref. 3, Eq. (26), when a linearly polarized wave with the

electric field in the plane of incidence is incident broadside ( 8 = 90 deg) upon a

thin, metallic wire, of infinite conductivity, the radar cross section CJ" is

given by

(5)

7

where

go - 2(sinx - xcosx)

y = 2cos2

x(-1 + cos2x- jsin2x) 2L(2x)}

·a + j2cosx(xcosx - sinx) (2n4 + n

X = kR = 2rr2 22 = total length of wire A. ,

n = 2En~ a

a = radius of wire

L(y) -ju

1 - e du = Ci(y) + jSi(y), for any variable y

u

Gin(y)= fy 0

1 - casu du = Qn(Yy) - Ci(y) u

y

Si(y)

Ci(y)

Si(y)

Therefore,

= 1. 78

=[ sinu d -- u u

0

siny· z for y >> 1

. y .

z TT cosy for y >> 1 -z- y

L(y) :::: Qn(Yy) + j; for y » 1

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1T When x » l and x ~ n2 so that xcosx >> sinx, inserting from the above ·

definitions, and neglecting higher order terms, one finds that

2 2 2 go 4x cos x -- ~----~--------------------~~~~~------------------------~ 2 2 . . 2

2cos x(-1 + cos2x- jsin2x) + j2xcos x{ln4 + n- 2in2"{x) + 21Txcos x

Since

Rn4 + n - 2Qn2'Yx = -2 Rn('Y~a)

then

2

and

go 2x

---y;; - 1T - j [2 R n ("~a)] for x » 1

;z =~~ =(!) (;)2 + x2 l

[ Q n ("~a) J 2 = 1T (; ) 2

(6)

Equation ( 6), derived from Ta1' s own general expre s sian, is identical,

at 8 = 90 deg, to Chu's expression, Eq. (4). At this point it was obvious that

the complete general expressions of Tai 's derivation should be used rather

than the asymptotic expression given by Tai. However, simplicity of his long

wire expression is appealing from a practical point of view, since the general

expressions are rather lengthly. In order to preserve the simple expression

of Tai (Ref. 3, .Eq. 21) a simple arbitrary functionf(e) is chosen that modifies

the second term in brackets of Tai' s Eq. ( 1), and modifies it only near broad­

side so that, for k 1 >> 1, it properly reduces to Eq. ( 4) or ( 6). That is

j(e) = 1 _ (sin (2kicos8) )2

. 28 2kQcos8 sin ' for kR » 1,

- 9

where f(8) = l for all values of 8 except for 8-90 deg, where f (8 )- 0 near

broadside. The new expression for the RCS of a non-resonant thin, long, -

metallic wire may be written as

l P(4;)

TT (;)

2 + [Qn('{k~sin8)] 2

X l [l ; co:28 sin(2kQcose) _ f(e) l- cos(2k~)cos(2kRcos8)] 2

4 cos sm2kQ sin 8

(7)

Predictions of the RCS based on Tai's modified expression, Eq. (7),

for the wires described in Table l,. are shown in Figs. 12 through 17 together

with the appropriate data. As can be seen, the modified Tai's expression

for the RCS of thin, long, nonresonant, metallic wires predicts the RCS vs

aspect angle for 4. 5<kQ < 17 within a few decibel over the entire aspect angle

variation, except near the nulls. However, for kR~45. 7, the predictions

vary by more than 10 dB from the measurements. Since the modified Tai's

expressions are simple, they may be used for quick and fairly accurate

estimates for the kQ values given above.

B. PREDICTIONS BASED ON VAN VLECK'S, ET AL., EXPRESSION AND COMPARISON WITH DATA

The expression derived by the above authors (Ref. l) was one of the

earliest in this field. Even though S. Hong (Ref. 4) claims _Yan Vleck's study

to only be applicable to short wires, our experience has been that Van Vleck's

expressions are of much greater general validity than given credit. This can

be seen in Figs. 18 through 23, which are the predictions obtained when the

parameters of the wires of Table 1 were used for the predictions. The

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cross section expression of Van Vleck, et al. (Ref. 1), is reproduced

here for easy reference. Note that these are Van Vleck's approximate

formulas.

IT= 4rrP(~) I (F' + F") sin 2qQ + 2(G' + jG") cos(qR) fsin(q + 13 )Q q . Lq+13

+ sin(q -13HJ + 2(H' +jH") sin(qR) [sin(q +13)Q - sin(q -f.>)£] 2 (S)

q-13 . q+l3 q-13

where

P(~) = asgiveninthetext

A. s-2' = 2 log -- I. 154 · e rra

2G' ljJ((3Q)

= ljJ

2(13R) + Z

2(13R)

TT 2G" --2 S1 f

Z ( 13R) = lJJ

2{13R) + Z

2(13R)

2G"

lJJ(13R-rr/2) rr 2H" = · z z -z~

ip (13R-rr/2) + Z (13R-rr/2) 2H'

ljJ ( y) = - ( S1' - ~ ) X co s y + ( rr I 4 ) sin y

Z(y) = (1 /2) (loge (4132) + 0. 577] sin y - (rr/4) cos y

11

A = -{l/2)[log (13Q)) + 0. 712 e .

q = 13 cos e

13 2 TT /'f...

'A. = radar wavelength

2Q = total length of wire element

a = radius of wire element

e = angle between line-of-sight from the radar to the wire element and the axis of the wire element

j = J-1

As can be seen from Figs. 18 through 23, the expressions used by Van

Vleck, et al., when compared with the data, give good RCS results for all the

cases shown except for end-on incidence. The difference between data and

predictions in all cases is within 4 dB at the peaks and within 2 to 3 deg in

look angle. The accuracy in the nulls is not quite as good. Tai and Van Vleck

are about equally as accurate at the lower k£ values.

C. UFIMTSEV 1S SOLUTION

The RCS of long, thin wires as given by Ufimtsev (Ref. 5) is taken

from Ref. 4 and given below. The predictions based on these equations are

compared with data in Figs. 24 through 29.

l. THE CASE FOR 8 ~ TT /2

4 I 2 4 cos q,. s(e)l

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where

S(e) = - s1n - · x.n . 4(e) n [ i ] 2

Yka sin2

(e/2)

+ ikL2cose 4(e) n [ i J e • cos 2 . x.n 2( e)

Yka cos 2

+ eikL( 1 + COS e ) 2 1· 4(8) ,1, n [ i J • • s1n - · '+' • x. n 2 - . (e) Yka sin 2

_ cos 4 ~~)·l!J+·Qn[ i (e)Jl Yka cos 2

+ cos8. £n (-i-)· [eikL2(ljJ )2 + eikL2(1 +cos e)(lj! )2 D Yka + -

_ 2 eikL(3 +cos 8 ).y; .y;.y; J - +

y = 1.781

ljJ = i lT- 2 Q n (Y ka)

Qn ( i2~L2) - E(2kL) e -i2kL Yk a

2 . ,~, ilT - £n(Y q±) '+'± = ---~-i-2k_L __ )---(~2=k~L~q~±~)~-~--i-2-q--~k~L---

£n 2 2-E 2 2 .e ±k2a 2 k a k a

q ± = (k2a)

2 ( 1 =F cos e )

E(y) ~ .[y c~stdt+iiy s in t d t - i 1T I 2 t

n = 1-l!J2

· i2kL

e

13

2.

where

a = radius of the wire

L = total length of the wire

e = the angle between the propagation vector and the wire

4> = the angle between the E vector and the wire

THE CASE FOR 9 = rr /2

2 (} ( e = rr /2, 4>) ;x. 4

= cos 4> X Is I 2 lT

S = i;; _ ikL (\ii)2

E(2kL) + A - 1/2

2A2

A 2

+~ [ lfJ _ .en(if2),l ,1, A 2 4 Yka J '+'

ikL e

-2 + 2(lfJ) X Qn (_i__) (ei2kL _ lfJei3kL)

DA2 Yka

l 2i ) A = Rn\Yka

lJJ = lJJ ± ( e = rr /2)

As can be seen from Figs. 24 through 29, Ufimtsev1 s re sitlts compare

very well with data for all kl values considered. However, the expressions

are complicated and the modified Tai may be used easily for the smaller kl

values. The location of the peaks and valleys compares well with the data

and the accuracy of the predictions is comparable to that predicted by

Van Vleck.

14

I I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I I I I

D. SDI TECHNIQUE

The SDI technique has been used by M. B. Associates to develop a

computer program designated as BRACT (Ref. 7). The BRACT program uses

the numerical solution of the thin wire integral equation to solve the complete

electromagnetic scattering problem for arbitrary wire structures. For these

arbitrary scatterer s, the program sets 1up the structure matrix relating the

incident field to the resulting induced currents and calculates the induced cur­

rent distribution on the scatterer. The currents thus obtained are used to

calculate the scattered fields. BRACT is designed for execution on the

Control Data Computing System and is coded in FORTRAN IV as released under

the SCOPE version 3. 1. 2 operating system.

This program was used to calculate the RCS of long wires, using the data

presented in Table 1. The results are compared with experiment in Figs. 30

through 36. As can be seen, the calculated values for all values of kR are

nearly on top of the data except for the two cases, kQ = 13 and kR = 34. 8

where the differences are about 4 dB. It is known that the data for kl = 34.8

is in error, and it is believed that the data fork£ = 13 is also in error, since

every theoretical technique applied gives more error for these two cases than

all other cases. BRACT was also used to calculate the RCS of a wire with -4

kl = 157, A = 2 em, and a radius of 1. 52 X 10 m («A). The results are

presented in Fig. 37.

In order to prove the accuracy of the Ufimtsev and Van Vleck closed­

form expressions for very long wires, the RCS of the long wire k£ = 157

was calculated using the expressions of these authors and the results are

given in Fig. 38. The results obtained by BRACT and the results obtained

by the closed-form expressions are nearly identical, being about 1 dB dif­

ferent at the peaks and following the dips very closely, although Van Vleck's

expression predicts much lower null values than the other two cases.

15

I I I I I I I I I I I I I I I I I I I

IV. CONCLUSIONS

The comparison of. the results of the calculations with measured back-.' ·, :'..,...

scattered data from var,ious' leng~h, 1thin, .. cylindrical ~onductor s shov,;. s th~t, of the four analytical expressions, Chu' s exp~~ssi~n yi~ids fair R.CS·~~ree~ • ment with the data only at broadside incidence. The modified Tai's pre­

dictions at all angles are within a few decibels of the RCS data for wires of

Q 2nQ 4. 5 < k < 17, where kQ =-A-, 2£ =total length of wire, and A= wavelength.

For larger values of kQ, Tai' s expression yields predicted values which differ

from the data by as much as 10 dB. Van Vleck's expressions lead to predic­

tions that are within a few decibels of the RCS data at all angles greater than

20 deg from end-on, and for all thin wires tested, namely kQ > 4. 5. Even

end-on, the predictions can be used as an estimate if it is noted that the RCS

should approach zero as e- 0. The predictions from Ufimtsev' s analytical

expression yield results that are no more accurate than those of Van Vleck

(except near end-on incidence) and in the nulls. Except for end-on incidence,

Van Vleck's approximate expressions are as good or better than all others if

one is willing to let the RCS approach zero at end -on by using the shape of

the last lobe in the pattern as a guide. In Ref. 8 it is shown that the deficiency

in Van Vleck's theoretical predictions at end -on are associated with approxi­

mations as published, and when the general expressions given by Van Vleck

are used, the deficiency of the theoretical predictions at end -on disappear.

In appendix A these expressions are given and in Fig. 39 a comparison of

the calculation using these expressions and Eq. ( 8) is shown for ke = 13.

The BRACT computer program, whose results are most rigorous,

agrees with the data within l dB and ±l deg. The analytical forms take about

one minute of computer time to yield results for a given wire for all angles of

incidence, while the SDI technique, competitive with the time used by the

programmed analytical forms, takes a little longer, depending on the length

of wire. Moreover, the general usefulness of BRACT becomes evident

should one bend or distort the wire under consideration. Then, as expected,

17

the analtyical expressions for the RCS do not apply to the new configuration,

whereas the BRACT computer program is flexible enO\~gh so that for the

most complicated configuration of a distorted thin, metallic wire, accurate

results for the RCS may be obtained within a few minutes.

18

I I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I I I I

1.

2.

3.

4.

5.

6.

7.

8.

REFERENCES

J. H. Van Vleck, F. Bloch, and M. Hamermesh, "Theory of Radar Reflections from Wires or Thin Metallic Strips," J. Appl. Phys. !.§., 274 (March 1947).

G. T. Ruck, et al. , Radar Cross Section Handbook, Vol. 1, Plenum Press, New York- London (1970).

C. T. Tai, 11 Electromagnetic Back-Scattering from Cylindrical Wires, 11 ·

J. Appl. Phys. 23, 909 (August 1952).

S. Hong, Scattering Patterns and Statistics of a Long Wire, Lincoln Lab Technical Note 1967-55 (December 1967).

P. Y. Ufimtsev, "Diffraction of Plane Electromagnetic Waves by a Thin Cylindrical Conductor, 11 Radite Khnika i Electronika ]_, 260 (1962), English translation, p. 241.

M. Rockowitz, Static Patterns of Dipoles, Lincoln Lab Project Report PA- 179 (March 1971 ).

RCS Computer Program BRACT Log - Periodic Scattering Array Program, M. B. Associates, San Remon, Cal., Project No. 00041 (January 1969).

M. T. Tavis, Van Vleck Revisited: The RCS of Thin Wires, Aerospace Corp. Report No. TR-0073(3450-12)-1 (September 1972).

19

I I I I I I I I I I I I I I I I I I I

- . - ___ __j_ - ______ L ___ - -· -_ __l___ -

01 POLE LENGTH 32. 0 em FREQUENCY 1320 MHz

l_ ____ _L _____ -

ki = 4. 44 -10 ka = 4. 2 x 1o-3-

'A = 0. 227 m

-20

E

I (\ en .a "0

/ .. -30

I V)

u £t::

-40 I

-50~----~-----r~---+-----1

0 30 60 90

ASPECT ANGLE, deg

Figure 1. Measured Backscattered RCS for Thin, Metallic Straight Wires, ki = 4. 44, Circular Polarization ( 9 0 deg corresponds to broadside)

ZI

' I

1 I 1· Dl POLE LENGTH 66. 3 em FREQUENCY . 1320 MHz

I 1 ki = 9. 2

-10 ka = 4. 2 x 1o-3 -

A. = 0. 227 m

-20 ( ~·

\ ; E ! \ UJ ..c "0 -30 .. V)

u ~

-40

-50 1-1----4----ll----1---1--+--____:_---1

0 30 60 90

ASPECT ANGLE, deg

Figure 2. Measured Backscattered RCS for Thin, Metallic Straight Wires, kl = 9. 2, Circular Polarization (90 deg corresponds to broadside)

22

I I I I I I I I I I I I I I I I I I I

-------------------0

~

-10

-20

E Cl>

..c:::l "'CC

-en c.,:)

. D:: -30 N w

-40

-50

/~ Jr\ !'

(\ I .. 1\ I\ -~ ... .A

" (\ '

l" I!

~ \ 7 '

.. .

~ )

TOTAL LENGTH {21) = 2. 48 m RADIUS = 4 x 10-4 m RADAR WAVELENGTH = 2/3 m

k.l = 111.7 I I

330 0 . 30 60 90 120

Figure 3.

ASPECT ANGLE, deg

Measured Backscattered RCS for Thin, Metallic Striaght Wires, k£ = 11.7, Linear Polarization (90 deg corresponds to broadside)

Jr\ I

•'

.

150

I I I

DIPOLE LENGTH 93.5 em FREQUENCY 1320 MHZ

I I kl = 13

.,.10 · ka = 4. 2 X lo-3 -)... = 0.227 m

-20 I

E t ~ ., en

..a "'C 1\ .. -30

l I ' ~ ' V)

u 0:::

\

. 0 30 60 90.

ASPECT ANGLE, deg

Figure 4. Measured Backscattered R.CS for Thin, Metallic Straight Wires, kl = 13, Circular Polarization (90 deg corresponds to broadside)

24

I I I I I I I I I I I I I I I I I I I

I

I I I I I

10

I I I E 0

en ..0

I "'0

.. V)

u

I 0:::

I -10

I I -20

I I I I ~--

I

) I I I kL = 11

ka = 3. 95 x 10-2

A. = 1 m

~ r ~

" I

n n ~ ~

" ~ N ~

~ - ·-·-·--- ____ .., ____ --- . - ···--· --· -

174 162 150 138 126 114 102 90 78 66 54 42 30 18 6 0

ASPECT ANGLE, deg

Figure 5. Measured Backscattered RCS for Thin, Metallic Straight Wires, k.l = 17, Linear :Polarization (90 deg corresponds to broadside)

25

E en .a .,

.. V)

u ~

10

5

v 0

;

-5

-10

-15

90 78

I I I k.l = 34.8 ka = 9. 1 x 10- 3

A. = 0.69 m

(\

I \

' ~

" ft

~ ... .._ '""

... - ...

66 54 42 30 18 6 0

ASPECT ANGLE, deg

Figure 6. Measured Backscattered RCS for Thin, Metallic Straight Wires, k1 = 34. 8, Linear Polarization (90 deg corresponds to broadside)

26

I I I I I I I I I I I I I I I I I I I

----------------~--

E en .0 ~

.. V)

u ~

N -...)

30

20

10

0

-10

-20

-30 90

1 I I I I EXPERIMENTAL MEASUREMENTS k.i = 45. 7 ·· (sigma· incorporated reflectivity range)

ka = 0.22 . -A. = 1m

..

"

' ~

n

80

1\ / ft (\ 7 \ I n h n ~ n " n (~ y

~

70 . 60 50 40 30 20 ASPECT ANGLE, deg

Figure 7. Measured Backscattered RCS for Thin, Metallic Straight Wires, kl = 45: 7, Linear Polarization (90 deg corresponds to broadside)

1\ \

'

10 0

ASPECT ANGLE, deg

Figure 8. Comparison of Tai' s Predicted RCS with Measured Data, kQ = ll. 7

28

I I

'

I I I I I I I I I I I I I I I I 1.

I I I I I I I I I I I I I I I I I I I

-50 .. 1:;·

l : : ; : i il : : ! :

-60

i :,.! E:.;T !.1. ~ I i.f

[ i (! ; ~ . ! ' : I ... ' ·\"1 ; lin ; ' H1 ! : ' ' t ;:·r : : :·!

i t t i I ' j tli1 ! ' ! I

I i ! ! rfh 81> I . Ill ; i i I i ' ~rl l I'' ;

! !·J •ll

20 40 60 80 100

ASPECT ANGLE, deg

Figure 9. Comparison of Chu' s Predicted RCS with Measured Data, kQ = 11. 7

29

;11i ill! 1'!1u!1Jiu1/:l !11

1'· i1iiii-Hi:[tt'l1·: !J!+i 111 !1

111

1/IJ: !ill r·;! 1:1: ~·: r::: ;::: ;::;~·~~ ~~n :-!~. itt' J Ld U. . ~ Ll.).. ~m· . . ~,.L ,;-:.. _, . :1-r:-:t-:-fh+i ++w. "~-.:. : h ,;-, *"~ .;..,_·~ ; .. c ; ~ ... :

::; i l : !: ! i j i 1 I ] IIi 11111 lj:!: i il . '.! I · · ll j! Jjl ifj, i i 1 i! i I 1 ;! ·;!: j '; 1 ; ::.: I; j, i':: ; i 1. :: 1 ! ; :; !1

:: 1ii' d1! li' fl:t 1ill 'il !ill'! 1iil !.: ,ill :tii •!1: lilt 1:!: ;[!' :!ii lij! 11; il. ~~ -20 ,.,,''I! ill' , .•• ,,, 'i\ ., .. , .. 'i·· '' ·I I •' j'l ,,, ''I' . ;! 1 ' ' '•' ''I ·!~' liij 1 l!';,lijl''l'il:j·!'·lil.:.t1 .::i!·l·l ... l·•li.l!'t:•:.!.' l'''lli'l.;j'''l·.,,,

! 1

: •• : : I 1.' ! ,I ,' ,: i i , . ; ! ; ,I , i i l 1 : ; ,! 1. i ~.:.... ' · · ; , ! l ! : ; 1 : :,' l :. ! 1 • 1 1 i · · ' : I ; · • ' ' · ' ' 1 i I I 1 l ' :I -- .;..;.;..;++i-!''+h~+H· -'--'-1. +':P _:_ ·~-c-:-L!- ·. ., , +H:h+:'

d-~! l;ii lill1lll! ;ij; ;!;;.~:~~ rqi ;;: ~: ~ili \111 il 1-· ! ·-··1:!.,1~.: ~!.-',:: .. ,; .. fl.::,i ;·:.~~.--l .. :.t .. ;,i~ ~-·. ··.1: !,[J·· ~~-~ ··' m fOJ il··· •.• ~, , ..•. ! 1 L· ••. -f.--~~-,-*,..,...,H-+1!-+ti+ft'-r-r~m-'-rl i ;; ,:1, !i'' itti'l: ,,:,~· ~~ ~u·· 11.,,,· :~·~.; ,:"~.~:~ ::u il : ~. . 11:.: '!': 1

::. ·~n· ,,., . , II ·I , ljJI . It II. F•: I' I',, II r . ','' I . . ': , ... ".' ! '.; :. i, '.:.' •.' ,· H+ ;.tl-L '+!- : ~ . . . . 1.4 . I • IIi I'. I I'' f-l..: . ..:.. .. :.,_" . . ' .. ! I; . ''

I '! :1 ';I :1 :rl·! tl :I; i!l.'l~l·l I: I I,,. I: I'! \'II IIi I i: I~:-.:_!:: I il! '' ·,:I: iii : '! ~ l.Li.l.i. 0:.1:: i: I: !,, : ..• ·~·'I :, !. ;, ·, : ii 1 ;11 ! !tl:::~~~lliwi :'1 !:• '!:1 ,:!, i'~l'\'ili '11' ,; i 1' 1: :L!.i~~;li :;:;

-80

f! ii ~~ .. , r

i ~-4-

-100 0

; i ' i i I ' ' l!ii ; !I

~ '.~ :

100

ASPECT ANGLE, deg

Figure 10. Comparison of Tai's Prediction with Measured RCS Data, k£ = 4. 44

)0

I I I I I I I I I I I I I I I I I I I

I I I I I 1--

1: I I

I I I I

I I I I

-20

,..30

-40

-50

-60

-70

-80

-90

:+-t: ....

-100 _;ii! )FL~ i 0 20

i I ' ! li.H l ' ; '

_, l I ' ; ,,

' ' ' i ' ' i I ' i ; ! l ' I ;

I ' i I i ! ' 40 60

;

.. . !: ·t:: --4·-f---+..;-:-+~ '". ~ l;; .i.~+i -~1 ;+

:: :: :-: -~ • i 'I " . . ; : .. ; :! i ~! l; ·! H· i ~: j :; l t i':-

' ! I ;·:. : ! : ~ I ' ~ : . :

80 100

ASPECT ANGLE, deg

Figure 11. Comparison of Chu' s Predicted RCS with Measured Data, kQ = 4. 44

31

·-..

r'-lt 1 i ;'!j:L;i: .:11 ,T" ;1 1---- icr!~l~ li :::L~\:,LJ; ;.rt-lrtli: Htt·!:!JL::-:: ;r--:- .c-c- i;·; ', ,,, Tl"ir ,;~r; :f ttfL 1+if it±T ·ret"+:;; r~n ~~ Tt': ll':s:ld~ sfJ.l~~fft-±tL g lt£1 -~i-f' ±W-iit± ;:rl

r!-Lii!J 1! -: t l'tlil r VLJ' ~--- -im- 1- t:b __ : -_nt.t ~_;rc: ji ! :t:-r:tt_' -I i j_t'· 1-_l+t'[t'-]trtl' --ffj-1':;;: :ll-,-1 ;t'!:f!J! J.i!·_-I:T, Fit; :: :.i : f-J i If-it''' '-I 1-,- ' '-+-·- ,_,_ --!!>-·j-' -: I jlli 1-j rf-1- ' ---+ >·r I ii-I "i'' 1•1' -80 '-IT ·-·r-··' 1 ·1-· lt · •·1 ; -'"---:--~.-t__l_ H~ !-:. )-J,}J .--Ill u ~l Tb.J.: -~-;-·---~-'- ··-• iH•· L ,. ':1

0 20 40 60 80 1 00

ASPECT ANGLE, deg

Figure 12. Comparison of Modified Tai' s Prediction with Measured RCS Data, ki = 11. 7

32

I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I I I I

Figure 13. Comparison of Modified Tai' s Prediction with Measured RCS Data, kR = 13

E en :8

-30 1::1 L'jJ 1 !LJ1'i! 1111 +·11 [CiiHI'Hij·'~:r-:::i - ,i'll~illl'll ~r-tr ltl !ltr! jJIJJJ!_. 1-It1 jt!"ltilt! II I ,. 1i I I I - ' ' i I I !ill " .I I'! I ! i! ' I :t i i IEJ !n_ ~Iii ' -! ! I - ! ~JH ,__ :-Hi t.;J I

!): i i ill ~ 11 jli II i ! ill i I !I I II i 1: il i I L J ' i i ll i ~ : 11!!1 ;_II fli j I i l ! lfi It i 1; II! !II It !II II ! : i Ill! Jill IIlii

I 1

1 *~;I :it~ .1;; 1.~ It! f1' ~ ;j i !lt 1 1 ' nl ·! 1 !~ -~r·;r !·'I 1.1·1i!) ... ll ··!! ., ·!! ; .. 1\'1-i~l ll!il :::~: :tli lrl-1· i!!i l_ii_! !ill:l ·~~!II i'l 'il· ::k: :ii!IJ:il ~~ ~~ ~~~~lilt: ~~~!1 !!il It: 1-H jijli •• ! ; 1-+1 1! 1 1:; ·'ltl ! I. i ' . j··tl' :! ' · r ·r, i 1. i 1 1111 ~ 1 ·l~ . 11 ·: 1 • ~ 1-i 1 l-n . t·1· 1 i 11 1

:!ii 11:1:: i!li W1 ·,: ·~: !i:~~- ill; :: 1

· 1li i : i::l 1ii 111 jrl!t ),_, 1

ibj :li11 l11l::i: ,1 I JHLj:H~ -40 :J!j I' : '·' ,~r:' I •'11''!-l'h-iL •1 . -: , .. , r • : i_l_- !~ t··· -~ll :!-t.\.'_r, ~ !t··-! ·tnT

r't' ';l:! :.: u:: ::!!'tit li!ihii f:t, ;i i i: \it:ltl-11! ib 1111 :.;1: 1::: i'1·-H rtq ··fi~·J'-JF+HT.-.;:, ~-· !'di --:·Ti-l-L., .. , ,,-, 11·! ... 1 : -·l -· .. -!:'I" -:-. :rr· :· ~· .. - ·-~ -.--~ 1l+

Figure 14. Comparison of Modified Tai' s Prediction with Measured RCS Data, kR = 9. 2

34

I I I I I I I I I I I I I I -I I I I I

I I I I I I I I I I I I I I I I I I I

j i ! ' i ' I '

! ' ! ! t ;

-90 I

' i ' ' ' f ' ; i ! l ' ! '

ASPECT ANGLE, deg

Figure 15. Comparison of Modified Tai's Predicted RCS with Measured Data, ki = 4. 44

35

kl= 17 ka = .3. 95 x 10-2

20

ASPECT ANGLE, deg

Figure 16. Comparison of Modified Tai's Prediction with Measured RCS Data, kQ = 17

36

I I I

I I I I I I I I I I I I I I

I. I I I I I I I I I I I I I I I I I I

E ., :8 .. tJ a:::

F~gure 17.

ASPECT ANGLE, deg

Comparison of Modified Tai' s Prediction with Measured RCS Data, kQ = 45. 7

-40 --1--- -~- - -- ~ --- I .. -~-r- _c r -1: : -~v~ ~t-~---- +-- ,~ ~--+ --~C •••• _

1 -_~_;~---_· .... 11--~ ___ - ;,-~- _---ri_--_-_-'-_ ~~-------_ ;4lJJ-.--- cc.: L -~ ~b~~J~

:1: . [{! ... -: :::: "·• :.: ·;. ::::. : l

r-:1 i.. :, ' ...

-60 T-:--:--l'- c-f--'-'- '-- -- ·-:--:-,-1-:-'-1-t ----cr---h-:--'-ft'-1--c-' :...,..: b . .c:.._ • +-:-'.-+: .·'-'-, .+, :.;.,-,+1 _--'-*,.,.:..;

. :· .. :i:!

---tc--t-:-'--1-·-. ~--~ ~-~ ';+- ~~f-... ,., .· ::' _ .. ,·

::.-f. ',-: . -~~~c-..:-'..:-. I···

1--'-1--'--if--'--l-'-' -1. __ 1_..:-' ~- ~':- ~'-. __:_c. . ! :- ·-r.---:+'-.-" +' _:-c. :b:-:-1--:-:+ .,-1---+· '-'-+'7+-=1-:---'--70 T .: • . . . . : : : sf.. . . . .. . ... . . ': '! ''' II

0 20 40 60 80 1 00 ASPECT ANGLE, deg

Figure 18. Comparison of Van Vleck 1 s Predicted RCS with Measured Data, kQ = 4. 44

38

I I I I I .I I I I

I I I I I

I I I I I I

I. I I I I I I I I I I

-40 ::' jj I! i! w ! ![ l :! !! : J! l i! i r ! i i! !! i 1 r ! l i; i ! q i; ! ; i i I u I :. ! nn j i . i it' 11T ' ·Uri Ji, iii~ ::l[ :!i~ iU: i!ii1ilil !li· li ' ·; i 1 fii HH T i_ 'Jrb' i· -'i:if i 1'~. }I h±i :iH 1-j'l 1111 i;jlJi[li:ii ±( .: I J 1!~_1/ 1if] c', IWt:J.ii ilJ1

1'. l:jjl 1! •·• • lj.j, • ,_. • , .. ~· • ~- .. ...,.:; H! . .._ J ~ jl •• •!, -ul .. -1 1:r. -d~ I!! ·t.f:tj

' r TG~ Uil ~!'llil' 1::.&:-'{UTtl_ :j ' ' ·· ·· .lf" irH i t ':i:H ::r -51.1 .• ,, .. • F' .. 1r111 IfH' r ,,., .. , .:tt. ·• .. ;Jt:Jf:f!it+t:l'tt.r.lt~t.' ·I···+ ''til:ii'l!:l .u j!Ji

-!-. r+-+- --4~ :t.!:! .tt.U 1n-r 1 ,... .r:;-r <~ i :it.. t:tt

1<1 !t~·f i+!t :Ht ~,·J: !rf: 'Jil h'1·: t H /ii :·1. wl: 1.111 :;; 1ift 1•11 Itt. n•t T' ~~-···· .rn. l ,~ 1\ 1, \P- I t\i" ~-ttti fl. HI '

1·r Ht w:H Ftf 1'-11iHol+JT 1>-1•• p:rut:;:r. Hf tfi! ,:It ·1iH i: ltt :· · '. 1~1, -70 ·!+· ,,.., ,,. . • .,'tt.iii ll jl '" ·t\! .

0 20 40 60 80 ASPECT ANGLE, deg

100

lr:

; 1

+

II -:r '.' . . Rl

Figure 19. Comparison of Van Vleck:' s Predicted RCS with Measured Data, k2 = 9. 2

39

E "' .0 'U

-10 .,; u «

ASPECT ANGLE, deg

Figure 20. Comparison of Van Vleck 1s Predicted RCS with Measured Dat.a, ld ::-: 1 l. 7

40

I I I I I. I I I

I .I

I I I I I I· I I I I

I I I I I

I I I I -I­

I I. I I I I

I

v; u IX

' . '

40 ! . --· : .,· : : .· ·: 'I . ! , . . '!' t---f---- -- ~ ~- _:_+-'-· ---· j - _L~ --+-- - cc:hc --- - - '-~r-.·_~·_j; 1-j....:l '--1---.J..-.:-'-4--. ---~· .:..;.4.;....:' '4' .;....:. 4. ~-+-'-1-i:.;,.'+' ...:....t-1'.;..:..+.:..-.~.;.:....+;_;' .j..!.,..,..;. ~~;_;.~~-·-H

301-:~:~:·-~·-~:(44:,-.;....:.'-'---,•'4 ·~·· ~:~.J.:.c{ ,.,., ' ' · =3~. kl = 13 ka = 4. 2x1 o-3

>.. = 0.227 m

:~~ ~~I.

~ cr. .:i_! POLARIZATION: TRANSMIT CIRCULAR :. ·: :

RECEIVE CIRCULAR ~~f-:-':;j :" . I

ASPECJ" ANGLE, deg

Figure 21. Comparison of Van Vleck's Predicted RCS with Measured Data, kR = 13

41

20

< ' : I : : : : ; ~ j i : : ; : : ; ' t ' u ' : : ; : ;_: : : : ; i ~ I ~: l ; :: it : ! il : : : i : ; i f : !·F it:J _40 ?~< cJ:: · iU ;::_: ;1:; !:.: :~· ;:: :,; i/: ti

1; rJ:i ;1:

1 IJ!I;b::::r:!Ft:n

'·.' .. _',- :_·· ... ·:-.1, •· '::: ·,'_,_:_: !: · ,,,· · , ,: : ,, i,',.:,ii,d:,';'l!_-:1,~ •. ;,,: l,l,\,H.•J,:i. !,1,!1: :_:,,Jl !.l_.t;',·

1-+~-Ci..,.~~'...L':J.''+.:·:;;) ii · ;· 't ~t lr!.r I·· 111·~1 -~;n ···rd ~·~- "~"L----,- -11 ·:··~· : __ ':: 1 ··,: ::_, :, ',•.;,, :_,· :_ :.' ;_ ,_' ;_ :_. '_

1 • 1 • I rL, i : :-:; ~: 1: :1

1 ~ ; : i ·1' U r. !,.11,1, 11! li !J•ni! 1•:;1 :_~:.Hi<;_: !,•; t. i1:~~ ;- :-t ; ~-i .; I 1 . 'Lr~-~ I ttl· 11 ~. t 1 1~1 -l+t - -~ 1 t 1-, +! r 1 ;-i ;~: . ~-· r +t-~-· -r-!-t

Figure 22. Comparison of Van Vleck's Predicted RCS with Measured Data, kR = 17

42

I I I

I I I I I I ·I I .I I. I I I I I

I I I I I. I.

I I I I I I I I I I I I I

60 ,[:I}: !!i! ~:~[it !!l : i, F! 1 ::: !ili It: I IW! !!!i' I: [J 1 lW [ u Ill 1!1 lH \li:

1~:: ': .· · i 1 t ::!.', ;; i il!i:,·:cu ::r::u !l ~~.[ill_, ~ · :1 ::r ;\· ; ~~~ :: ;;1:H' ,,' r: • ';:i 11[! (, '~ lill [ll_ifr: 1\'!! \! IJ! fill\ U j~ it lH r li;l ' 1 :r:;n ii ·::: !c.· :' + vAN vLECK · · · · · · lili· ' ;

50 ··:; :::, ,·' . : :r:, ·. 0 DATA :.''!,' 1:,;_:_· ' • : ; I : ; ! ~ I • : ! I : I i ; ; I : : ~ :

::J 'li !•; :" ','; i kL = 45.2 I il!: :i 1i b~\~: I ii\U' i 1 :i: ,' ka = 0.22 11'' 11:. !" 1!::! 1!

1, r~[qj)jll:: ll: i >- = SET TO 1.00 m !Ji~ 1 .

40 tit!! : ';i 1 •ri; '

1 Ul 1 POLARIZATION: TRANSMIT LINEAR 11

1

, !1[1. '•!li' !i RECEIVE LINEAR i-! : i irtii i ! i i fll w I i I Hi ' ' rffim;:mTim:rr!:ttl:m:ttttttm ~!/t, ' ' ''! I I : HL 'Ui I

30 '' '

'i' jl

· r: i •. r~t; 1 1 ~ · , · , 1 1 ~ ' 0 :n; . , . 'I !.

u i: i I 1

I,

t1 liF! : • I:; I ' -20

' p! . ''L} i · .

-40 tit. 0 20

i '

40 60

• , I

Fr+ ' '

80 ASPECT ANGLE, deg

I ,

100

Figure 23. Comparison of Van Vleck's Predicted RCS with Measured Data, kQ -= 45.2

43

E en .a .,

.. V)

u ~

* UFIMTSEV

o~++H# o DATA I k.l = 4. 44

I+H-41-'-H-H-

I I ir'il ka = 0. 0042

! 111 l i : A. = 0. 227 m

; fl=·

It f~~

IJ..· : it r J l ~ L~ i-1

-10 · i1! 1 :!!:POLARIZATION: TRANSMIT CIRCULAR-;, I ,_RECEIVE CIRCULAR t+H+t+t++lt t1 · . Tt+'it'l t:+r- 1-11 1

-+· . :r.rtiL :H :~ U: I ' T':·l-'i : :+ F;:., ~r; 1 : :t · 1

fi ' : :l(i~ ~-- d::t ,:s--ic , • -•- "'l ii=H + ' ·.. .

' .... ;~f.!: -- · .. ' : ~!

-30

I

II

iII ' I I '

I ' l -40 I ·I

I '. ·I

ASPECT ANGLE, deg

Figure 24. Comparison of Ufimtsev's Predicted RCS with Measured Data, k£ = 4. 44

44

I I I I .I I I I I I I I I I I I I I I

I I I I I I I I I I I I I.

I I I I I I

E en

.Q "'0

.. V)

u 0::

20 40 60 eo 100

ASPECT ANGLE, deg

Figure 25. Comparison of Ufimtsev' s Predicted RCS with Measured Data, kQ = 9. 2

45

ASPECT ANGLE, deg

Figure 26. Comparison of Ufimtsev 1 s Predicted RCS with Measured Data, kQ = 11. 7

I I I I I I I I I I I I I I I I

I I

I I I I I I I I

E en .a ~

.. I

V)

u IX

I I I I I I I I I I

* 0

' : : l! ; r: ; :! ! : 1; , , ; . ; ! : 1;!: :! 1. II· ! 1 tiiJ I! · 1! -. llJ:! II!; 1 1 : 1, ·1, i: !· ·1)1 ••! ,,,, 'I• llji j·i·!l 'il, J!ll 1 • JIJJ l:j ·j·j!j,].;li ·HJ'II:.•I I·J· 1·: :+ ,. "! t!· ;•·;I ;,·_ ·, . ·!-i-1 I ·I; -·~; If ••• - -1+1 :. •t-"1: .. I ~-:~ .. I

:; :t:,:-r· 't.' .!Jill r:: -:-~:t·tf:ttl- i·!t!T:'r -1-'L! ·t'-li'r- J.H-u•:'tt f'lt:!-:lti_tJ: j::Ji It!~ " L: r ! .-! i-:-f. ''J !-i·i r + -1 ~ -j.l-lj '. 1- tH;-• ,-r-!-i tq. L. ; I t-1 i-1+1 .. " 1'1~·1[-1 I ;. ~-- ·r · r-•·r ~-~- · ;~. :·t·l+ ...J.,-t- ·II I H·t-H-t!- -~rr H~~ " '-Hi-HHH· .:+.··Hi-!.

UFIMTSEV [1:1*1- !-!- 4 l·:.t-r-h !' ··r ·i ..1... -,

:f:!:j·Li ±j:+f Li::i±frcr DATA

13 kl = [l:fiiit[ m+~+t~

ka = 4. 2 X 1 o-3

~~: tg}. ).. = 0. 227 m

10 ~tn-::~T.. POLARIZATION: TRANSMIT CIRCULAR - ·:r rWt - f8_:~~: RECEIVE CIRCULAR EmJJ.. ·rtt:·:J~~,ft~clf±!: Htj: dif r,+rFJ :FiJf ~rf:l: t;ti HH:bEl:rJ.i:!EJt:J:Hc"~- ' - +H++i~:t=~t~ :ttt-_--,'+:EF.-:r~+-tf+r t+it 1-r-;-1- H~+.J:,.r-r~ r,-·!- ++~-· ·:·1+·:-+;·i· ~q:f-.:t:;t+~tffi=F-R+ ::P~+:~Tl:t:p:~ X!:f~r-4-

20 40 60 80 100

ASPECT ANGLE, deg

Figure 27. Comparison of Ufimtsev's Predicted RCS with Measured Data, kQ = 13

47

"' V)

u 0:::

Figure 28. Comparison of Ufimtsev' s Predicted RCS with Measured Data, kQ = 17

48

I I I I I I I I I I

!

I I I I I I I I I

I I I I I I I I I I I I I I I I I I I

E en

..0 "0

ASPECT ANGLE, deg

Figure 29. Comparison of Ufimtsev 1 s Predicted RCS with Measured Data, kQ = 45. 7

49

0

-10

-20

-40

Figure 30.

40 60. 80

ASPECT ANGLE, deg

Comparison of BRACT. Calculated RCS with Measured Data, kR = 4.' 44

50

I I I I I I I I I -I

I I I I I I I I I

I I I I I I I I I I I I I I I I I ·I

I

E Ill

:8

:'

i·j 1

' . . ! I: : ;. j l.

• ;c; I li: 1' I ' · ' ! , 60 \-;j I ·Ill 1 • • , 'i 1

- iti k 1· i I. ' : Iii :il H' I . ,, ~~T' ;i! I

: . . . ! !' I ' !! ! I i ,, I ~: :;I 1IT . i l ~:: : I :;p : ; : • . : i

_70

1iJ:): · ... i! ':· :. · :: :: :: 111 1 , : r 1Hiii 1 ',iii ; [!i ::: •i· i£t:'::·,~ ·,··!!, :i:lH 1 1,,,Tr r·~~~ 1,;:ii:IT,1F i! I ii I' I . ' I' ' . i I. . . : . . n· ' ' rr;' ,_; ill r;:·· ii ,j;! ,' II . ' : I: I I I !: I I!;' ! I :: Iii :' 1:; !!'i :;!; :i: ,Ill 1; I ii~ Iii :Iii 1:1!1 1 11 iii 1!11 i {, i ·::~ 1 ;

-80 It+~ ..... ! ++i-'+./..f+++1-H+I+H++++I H+ll v BRACT l I '

,).: ~~~:~ I I • 1 kL1

= ~.~TA ll@ !I! :, 1 · : i 1 , ka = 4.2x1o-3 !,~J;

· !1[ ! ' ; · 1 I ! "A = 0. 227 m : i - 90

1 i ::

1•

1

·, :I POLARIZATION: TRANSMIT CIRCULAR :n,· :. 1 ·_ I ! 1 RECEIVE CIRCULAR i :

-100 0 20 40 60

ASPECT ANGLE, deg 80 100

Figure 31. Comparison of BRACT Calculated RCS with Measured Data, kQ = 9. 2

51

-30 ',, : .. I; .• I' ' I H ' u i:'t I'· '

' , '· ~r . f!!J· '£!

· , I • i;rq~~~ , ,, rc'' rH::!f 111

i ' ' !

i I i I ! I I I I li i ':iii . fl ' iii ;

-90 0 20 40 60 80 100

ASPECT ANGLE, deg

Figure 32. Comparison of BRACT Calculated RCS with Measured Data, kQ = 11. 7

52

I I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I I I I

ASPECT ANGLE, deg

Figure 33. Comparison of BRACT Calculated RCS with Measured Data, kQ = 13

53

ASPECT ANGLE, deg

Figure 34. Comparison of BRACT' Calculated RCS with Measured Data, kR = 17

54.

I I I I

' !

I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I I I I

ASPECT ANGLE, deg

Figure 35. Comparison of BRACT Calculated RCS with Measured Data, kE = 34. 8

55

-10

E .. .D -20 "0

.,; u. a:.

Ul, C' -30

I F ·gure 36 Comparison of BRACT Calculated RCS with Measured Data, k1 = 45. 7 1 •

- - - -- --- - - --- - - - - --

-------------------H' 14 II,-_· +--H,.,--+·-I---+:...;_+-'-11r-~-11· ~rrl,"_:-1 ....:.:···+-t---'fJ-·~i'~,..,t-k-i, -r-· ~ ~i RE~uLrs ~ THE BR~CT coMPUTER PROGRA~1 ~,..-

-15 :I~~·· ~ +- .,.Jc .... I .. I I' -+-t--'t-t-:-'._·'+1- . •.·.·.·. -.~ .. OR. · ... '. kL .=,_ •. ·.'·.~"'.7.·r;c -... '.•""_:·,_. ·''·'· .. ~- .... ·-· r:--r--:-1 , · . ~r·- ·-r :•:·" L l. · · 1 ..

I'H-"-:T"-t-'+-:-:-T-'-t-ti:rTc.; t-' cc--r----r:- . . . : l '\I : . +-:-'1-"-+'"-+-:-.. +.' +".-:-+-:±:,.:f-'.:.:.t'-=f:.:....r'+'c't-'-"-f"-tc:--t-. -:-:-" . r .. -:t ·.,.T-:-r--. :-j--. • : -1:-:-" F

-20 ·: : -':, i:i ::, ~~ j .: ...... : :. : •••. :\ ••.• .• • :· ••.••..• :•,, .::· .. . .. .... .. . • ..... ·::' •·•·• •: •••.•.••. · ... . ,•:::·::r• ······-·· ii"••·· ... IAIP'!"'Il;••·· :::·· ······:•·• r' ,, ... .

. . ... :~·::I~:: > , .• ··~~ .·· I .. : c] .: , ::,- . ., .... , ., , .... . ····· ....

-25~~--~··~···+~·3··~~-+.~;_ -.,+.~+-~.~ .. r.~.~~~··~:~~~~~--~~~~· ~--~.-.~:_--.+_x~·~~J~-~._.-*··~--~·+=r~J,··.~~~·+~~;·•4,+:.~t~:!~;:.=.=,_,r~7~~--"' . . .... ,;: . . .... .. :••.[! : ·, ·.~:: .... :, ': ": .... ·_•: :_•:_:~·.• . :· 1 1'1 -1 _. 1. . ·· :• '.•.'. r . ·:: :o. .. i .J ., ·. li_.: ' "·' "f:..cur\.~+--1

&:-4·-'++~a:,+.+-t--i.,..+:.::r-+:H~T~+-+-:-'+--·+~"'t-' -· '-+--__ •.· .... ··. :: L IT'_ : ·.'.',· .. T• ·.·-.· ... -~ ...•. ::. ::: :;.: ·:;: ~~iqj _::.: ·· · · .... 1. : ·.:)·· 7 t"'!J" • :a .'t:ll

-3o . .. . .. .1 .. ... . .. .. . ··· ·,1 ;• !i': . .., . •· •· 1

-· .. :: •••• ;:~: :::. . .. . .. .. ... . :·:+--r-'11-· .:-'+-.i..f--t'·,.._· r'c'''+' ·.:..:.,··r-··..,'·t .:..:.,"cr-'"--+"f'i----i \'-c.~~~ : ',·.• ' :~:: '::_:_ .•.·.~t:'--JJ ...... · ;,; .,.·: ·JJ>:: .... I I: \:c. :: : :. : :J:.

-40 • ·.:.;J~+.±+c-:-1'-':'f:--:"1-+-t'~''--t---f_l_•:·t·'-l<i,...:.:. '~:t' :.;.,::•t'••_'·t ·-+:-~:t--tir--·f· --+·· - r-- i - __ ,!_..,...... •---..- r-:--• c-- ... :---t-.::t-'· ·- ~-.-: 'I ! i T. i

H~~::;.p+-':'H. :.::.: .. + .. :.:: ... ·f'-. :-'f. -:f~-rt-J1 .~ r-.. --- --; -r-· ~.. ! - --~~--~-.t:-1 ~- __ ;! ____ L,"':l1

1 ,

... · ·•· • ·• ,." • · .. ·' 1 ..1 ·1, ,

I. I .i ... -· -.,.-,·- '-~~ ·--11 .... -+++--1-+ 1-'--F

.· ..

-45 ... • • . .....+:-:4b-.,.f'-t--b--+--:-t--·r ·-:-t: • --t -+- · · : . :i --l---1-i- ~L _ l:-c-f-"P.+-·-'1".:.':-.":Fb-:..: :· ..... + . :! ····t'· .. -_r -.. r-'1-· ..... -! I i I b ' ..• .• :::: :::: .

... ': ....... . - ...-.-!--:'-+..:'. ..., '; :: : , .. , ...... .

". :::; ::

Figure 37a. BRACT Calculated RCS, kl = 157 (She·et 1)

\.]l

00

E ,.

i -35r··~··r'··~~~~~~~~---t·~--t·~-t-~---~-·t•~:::+'~'~t'7~''~:~::+:·~·-+·:~·-+::~:·+·'~::+''+"+i:+.··+·-~-·+·~·+.··~~~+'~··+·~-~~~-~-~-~-~~~~-~-q-~IPJF;h~ .,; .. : ,.. .: . . .... ... . .. . .. . . . .. .... :: : ..... " . .!.: ·I :: ; .. ·- . . .. .

~ .... . . ..... ::'.' ·: ...... ' '.:·~ :· ·:·. :;:: :•:: '" :·:: ::: :'fr: .. ··:'•::- :, :· . ·:. ~- . ... .. "::J. ....... -

:~ ·. 'P .... ~- I iL · .4-. :•· n.:: .. '; ;;; '~ ,:;,i· . !

~1 ,::: ... · · · · .: '" c; ;:: i1l_! IT ,. : .. .,; : .•• rl:: : .. - : ::: l;j •; •:i!l!f : : ·~, ' . : ·.: "' -

-45 r. __ ~:ii:. -'l _____ ~r ___ -f:_-l_t'·. ;_t-•.. ~~---'-1-r-•. _.:~:_.!~;-:._•tt-tJ~Jr::'tl:~ ·•"-~':If-=~:"-~', ;~'' w, '*.; ~·~;·*'-*_ .. +· 'i"'lh-.':-+>~:.rn-"-41* ... *. *-_4 __ ~----~RH+.-·4; ;4,· ~:.::.J_: .;..: ~-f::::·:.:t._b· .. f.:,_-•_4:.:_ ~._._:_-~.-4-.~ _-""':.:.·.~~---•_·+·-···:_·.i.:_J ::1 !·"!' ._.. ;; ~~~~ ~i-~ : :; :::.; .. ; :::: ::~i ; :· .. :: ··- ... :-.

.... t-·· •••• .. .. . ·-·· ..... ,. : : : ~ : i . -- ..:r ·::.L: .

..

'I .:j. ~·~-~~-+·~·tt~·~·+· ~~-~-+H~-,+T~'~.~;:,~ii~'~~8~--~·~~-~b+

-55 tt-H....wt--+"-'tt+ ... c:t. 1-H:\--'+"-llr+.,J-H-+-:-:-_J.:..:_ .~+:.c"~.f:-:.,.f*!,....;.: ,+· .-'-:111-. ·..;.:;b.::-"-1. I ~,.:.+.J.+;+m;..:;~~Fl++..:.:..:+-+++...J..--'FH~~-:.:.:-·W

. .. . .... • I . :•: :·~: I l . . .

-60 u . j >; 67.5 69.5

t:: 71.5 73.5 75.5

' i;: .· . .

77.5 79.5 81.5

ASPECT ANGLE, deg

:!: ::.;i: ..... .

·r 83.5 85.5

·Figure 37b. BRACT Calculated RCS, k1 = 157 (Sheet 2)

87.5

•.:: :."f:.'.

···•, :::'·II:: 89.5

---··---- --------·····---------- --

I I I I I I I I I I I I I I I I I 1---

I

E en

.Jl "'0

Or-~~T-~~~~~~~~~~~~~~~~~~~---~~~----~--~------~--~----------~-----~L--~----: ____ • ____ fl-i __ ·_ ·~---J ·1-T ________ , ___ J ___ t ___ J ____ ~--+-------·- ~---L- : __ __!-: l . -~- -· ;----. l · - . • I l ! . i . i ! , . - i --, -- 1 --~- :

-+--+-·!--+:-· -+---~---+-----+----+- : , ··-----+--;- Ij f -- : . I' I I I .

~--- ____ , __ · ·------~·-:-:----·-- ~---- 1------- f--· --r-. t-:·:·+--~---i-----. -L--j--1-· .J--r-:-~----

-10 ~I I ! ··1---~)il!.· I.· :,:,···.:POLARIZATION= LINEAR ______ L ___ _L ___ _; ____ t_ __ ~-- ... i..·--. ~~nt ... l ' ! I:! • •··• ' ~ ~ i • -•--~- ~--~r-- e.----:- f-- ~~ •---~---• WAVELENGTH = 0. 0200000 m - t- ~- -t -+ ·:·-:- r---:- _ !- __ _

I . 1-- >---- -~WIRE RADIUS = 0. 0001520 m ----+----

1·----+------r' -".·---.!llf.;..--J-. ___ j._ ____ ~---i 1 1 . .

-20 > !j - f -:-~ ! - 1-- k.l = 157 .! -~t. -i-----l- i-- 1 ~ --;---

1 '" .· VAN VLECK CALCULATIONS AS---+---- ---t----1----i- ' :-- --+-----

1 I . INDICATED BY "+"SYMBOLS i • I l I . : - --}- --- !-- --+--- --1 f--·- 1-----1--------:--·---- -· -1------ 1-----~ f----. ------• 1-'--t----+-- -- - i - +--. t· ---- i·- --+- ~ --- --- -; ... -~----L ! 1 . • i . UFIMTSEV CALCULATIONS AS i 1 i ' . i 1 • r • · A · -! · DENOTED BY "*" sYMBoLs -----~---1~---~--r -f- .... .J ___ _ . --: a· . . . i , , .. I

-30 .__: ~- i - . :~ p fr+ ' ! -r-_ ----;--;-.• --•. ·· :----r---t-~·~--,---··-~-r~-L- Fr_::r~~ ~>--· .• -.:: -

f----i- -~--- -----HlH,-----~~-_.J+.-!!II+l j I 1 ,,-=-+--,---1-~--~+----+----t --;---_----+!_-- . ~--•--- ------,----·-+---+·- ;-- r·- ,-- r---+----i-- -~ -- ' l :, --

•• _ __._ ___ +-· --!-+K-....... --f.~+----1~------+-1~·-fo-E-1 li----'-Jf-411--l-tl-..--1:-..-+~---'~--+-·-+---!---~ ~--1-----i---4-----·'---· -~--- ·-t- -- ---r . . · i 'j I. · · . · ! j I ~---- ---1-, .. --'-------1-~.,.~-----114-8- ·-t -·-1~-----...... ~·~"..:II~W-M.---,.__,---II(-,adc-,---.-!--·--:-l·: · --t--· 1-:-:-.:_1-~·_;...:~. ~-: . :-- -+- ·· 1-- . :----- ~- --+-----

. I

·' ~;

J-.-.:...:..j------ 1- -- +-- -;

-40 v; --+-+-:+!--·-·Hfii-!---Hrl-t---IH---+f-~~·1~..!1-¥t-IJ..li-~'~---H--tliii-A-,..._.a.:..JI--&-·......_~h---l-..:. ' ! j • ~ j - 1- ---~ --- ... - ·--l---+-------,r-'A· ...........

j-+:--· ·_1--M--+--·-·~--·· -__..._•·_-_-:-~~:-1-l!HI'.IH-:_-J-'--~--N, ~-.q. · W4-111-iH--I--f.'I-I--H·II-• ... ~11'9J---fiiJ-~ l-"'~ H' •. ~----r~n~nl!l1tt4~~~~~~, 1f•, h11

1ll·1 ~~· i . .• ;

u .. - --!'--------1-- -

0::: T- .; -!----. 1---· - - --- .. , . - ~ - :---+- -

50 ! I ~ • l • : ' • . [ L.l i _ 1---+-: ·------!---+-----!-ll-r----+----1-----~~----l·~~.J~·:.-1 II-4<U.:......-K--1J .. ·~tt-Hit'-fl~-tt-tlrllt-ttillt-Jit-·ftHH·-IIHIHf·~.--tt,..._lt-:ll~ ............... .._ .• J..-8--..._... ·, .. r·-·r.·· -- I::;,>··---"----!---

---+-----,.___ __ ,,___ :·· r-J- .: 11 w''t ~!-i: --- h:- - ·t • ; :l :' • • ' . .. '

~--~-~-+--+--+..._t---hll-+--t~---+t:--~1-+. •_...:. "Hii--.;..t..::' . .:..t~ '' t:-:..JI+-,--li-:..JIJ;--I~_._........_u ... ...a.-+&-~._.._._~~ _._. ··~J.;.~;.-t--+-t ,._.. ___ ------ ',.IL__, ... ..._ ___ i, -·. f--- ·· . :-

: . I . • . : ' ' i : ' I . j i ,i I.· .. : : 1----- ---11------+-----+---.-+---t---W---+-----&-----~J..- +1.1---'--tw---,-.~-;--'-l-:......ii4~ .. 1W-4 .. ·~11r-:1~1F-1'_.~~1-11~-IF--II---I---J---t;l--~l-11i-=t--:-l-...:-+ -i------ -~ i · . - --- 1- --•- -

-60r-+-+-~-~~~f-·-h~~-~~+':~,~·-l_·· ~:~:~~~~;~r~~j~~~~~~~~:1~~~~~~~-..:.~--~~~~~-_...:.~ j<:•i . .•• _,1·. .i ., •• , '.;I··-; I' i . -:•· ·I· . ! i, 'IL

. : : 1 :I>':;;. II I' ..

1----+--+----f----+--d----t-----l----t---l"~-1--'""----'+, .,.,, .· .:...:--l:.l!f----1 i.:..j, :. l-q; 1!1--tl , ...... : I-!-"' i • ' -- -.:. 1-- !---- --- ~- '------ . ' -- ···- ------: :; ! ; : '' i i ': i ': I ': • . . .. - ':: . : i -- !--~- H :'

. • . , : :. .. , I. ; , I ' -----·J..;.n~-_4----l---+--1

- 70 ~-:---. +-.---~-l~---------~---+----ll---:··~=:=· ,_ -+. ~--_·---··· +-~l-_·_. --~·· -~~~-:-~:-,r-:_--~~. + ...... ·~--:..:..• -+. t--:-1...,. •. -'-_, •• --+ .. -t~-----~:~~~:~:=~::~:-~:~:~=+~ -_·_ ~1:-~:--_-· __ · __ ~~-~-:~~:--_--· --r+ . I - - , + :~ --~ ,~=>-- j~ : t-f--t·-f_-+· .. ·-: ·J-+1--'--:-' ___ '--·:1 -~:==+-1--.....;.--., .... ___ ·_-·+f--------.~ I-··"'"·.·~·· .. ;._ .• r.-. ,c.:.. -H-. ~; ·.._;_.--'-+-1 . .....;.' :-:--!: ..;.,..,...'+--. -'-. ~- -+---'-,-+--.. +----------f-'-----1-tr.--.-._-·:-f~-~:=:=·~~:-~:r------~j----·_-·--~-~·------l-----:"r'·:·-- __ -- ----lt.·_ -_ r,· ------+-·:·~- _----+'-P.,.:.... __ ~_-+· __ --. ~+--------.... -7 ... ~--------~--' •. · - . • · ~ . : f: : i : 1 • ~ • , , • • _ _ _ __IL • • ,

. . . . . I; ' . . . . --.. . ' : ::.I')' .:1::.·. -,: ,: - .. i:··· . . -!~------ I IJ ·t-· ! : 'I I' , : ;~ · . . : --~__:_- ._:_:_f.--- ! ......... _ '.... ----J--

;1' :: ,::;iJ;!lLUJtili:lHlll·., : :r•' ·::: .• • l:i,. l·' • -J: :: ··- .. l. \ ·. T ...:::. -so~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. _.~~~~~~~~~~~

T - . !

. --1- -l --+-

! -·---l'-'---+-·-- f-- ·+ ---

: , ..

0 10 20 30 40 50 60 70 80 90 100

ASPECT ANGLE, deg

Figure 38. Van Vleck vs Ufimtsev Predicted RCS Values, k.f = 157 59

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-10

H , . m . .· ... . . ,:r : : ~k1 ;;::, · : ;- : .. : H-\· ~ : :- r ' • ' .

l ! ~' i-t i f' : ::r ~;t !

H: t-~ .· ' . I i I E en .a

"'0 -20 .. V)

u ~

-30

: !J :

20 40 60 80 100

ASPECT ANGLE, deg

Figure 39. Comparison of the Generalized Van Vleck Formulation with Van Vleck's original Expression, kl = 13

(d

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APPENDIX A

The expressions for monostatic cross section from a generalized

Van Vleck (Ref. 8") theory would be

E1

::: sin 2q£ _(A+ B) sin ((3 +g)£_ (A_ B) sin ((3 - q)£ cos e 1 + cos e 1 - cos e

9 ::: 13 cos e

21T 13 - } ...

A ::: 2K cos g.£ - (neiq.R.

- (Eeii3.R. 2L cos 13£

B ::: 2 iK sin q.R. -.(Deiq.R.

2 iL sin 13£ - {Eeii3.R.

F ::: Cin 213£

+ Ge -iq£}

+ Fe -i 13£)

- Ge -ig£)

- Fe -i(3£}

E ::: F - Cin 413£ - iSi4131

G ::: -F - Cin 2(13 - q).R. - iSi2(13 - q).t

D ::: F - Cin 2(13 + q).R..- iSi2{13 + q).t

A-1

(A-2)

(A-3)

(A-4)

(A-5)

(A-6)

(A-7)

(A-8)

(A.:.9)

(A-10)

L = 2 1 o g 2

( 2 a£ ) + 2 1 o g 2 + ~ -. C in 413 £

sin 4 ~£ - 1 4fH

- i [si4fH +{cos 413£ -1)] 4(3£

K - 2log2 (:')+ 21og 2 +~-Gin 2(~ + q) £

_ C · 2( A _ ) _ sin 2( 13 + q) £ _ sin 2( 13 - q) £ m t' q £ . 2(13 + q)£ 2(13 - q) £

- . f S"2(13 + )l +5"2([3- )£+[cos 2 ( 13 + q)£ - 1] 1 ,. 1 q 1 q 2( ~ + q) £

+[cos 2( ~- q)£ - 1] I 2( ~ - q)£ J

-cosy dy = ~ ( -1)nx2

n y - L...J 2n( 2n) !

n=1 0

Jx co . L (-i}nx2n+1

Si x = 61ny Y dy = ( Zn + 1 )( 2n + 1) ! n=o

0

£ = length of wire

a = radius of wire

e -- angle between the propagation vector and the wire

-cp = angle between the E vector .and the plane formed by the wire and the propagation vector.

A-2

(A-11)

(A-12)

(A-13)

(A-14)

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I UNCLASSIFIED s Cl . ecunty_ - ass1 1cauon

DOCUMENT CONTROL DATA. R & 0

I I

(S•curlly rlaa81llr.•tlon of title, hndy of fltbllltac:t 11nd lruJ,.,dnf1 annotation mu11t ''• enterod wl1ttn tl1e ovttrsll ttlputl I• c-ln•tillled)

1. ORIGINATING ACTIVITY (Corporate author) 2B REPORT SECURITY CLASSIFICATION

The Aerospace Corporation Unclassified

El Segundo, California 2b GROUP

3. REPORT TITLE

I PREDICTED RADAR CROSS SECTION OF THIN, LONG WIRES COMPARED WITH EXPERIMENTAL DATA

4. DESCRIPTIVE NOTES (Type ol report and Inclusive dates)

I S. AU THORISI (First name, middle lnlllal, Ia at name)

I Jacques Renau and Michael T. Tavis

6- REPORT DATE 78- TOTAL NO. OF PAGES '1b. NO. OF REFS

72 OCT 01 66 . 8

1- ea. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER($) .

F 04 7 0 1 -7 2- C - 0 07 3 TR-0073(3450-16)-2 b. PROJECT NO.

I c. 9b. OTHER REPORT NO(S) (Any other numbers that may be assillnec' this report)

d. SAMSO- TR- 73-136

10. DISTRIBUTION STATEMENT

Approved for public release; distribution unlimited

I· II. SUPPLEMENTARY NOTES 12. SPONSORING Ml Ll T ARY AC Tl VI TV

Space and Missile Systems Organization

I Air Force Systems Command Los Angeles, California

13.1 ABSTRACT

I In order to determine the validity and accuracy of Radar Cross Section (RCS) predictions for thin wires, the predictions of the closed-form expressions developed by Chu, Tai, Van Vleck, et al., and Ufimtsev have been compared

I with carefully measured backscattered RCS vs angle of incidence for various length thin, long, cylindrical conductors. Further, the prediction of an open-form numerical analysis based on the Source Distribution Technique

I and programmed by M. B. Associates as the BRACT computer program was also compared with the experimental data.

It was found that ( 1) the BRACT computer results agree with experiment 'so

I well (within ±1 dB for all reliable data) that it may be used with great confi-dence for any length thin wires and can be used as reference data for compar-ing with the prediction of the close-form solutions; (2) the results of Chu are

I not accurate except at broadside incidence; (3) the results of Tai compare favorably with data up to kl values of about 17 if corrections are made to the approximate formulas to correct for broadside incidence; ( 4) the results of

I Ufimtsev compare well with experiment for all k£ values considered; and (5) the results of Van Vleck, et al., appear to be very accurate for all k£ values considered except for near end- on incidence. In a separate report to be published soon one of the authors of this report (M. Tavis) has

I shown that this deficiency is due to numerical approximations in the theoretical expressions.

I DO FORM 1413

IFACSIMILEl UNCLASSIFIED. Security Classification·

UNCLASSIFIED Security Classification

u. :KEY WORDS

RCS of Thin Wires Analytical Expressions of RCS of Wires Wire RCS Computer Predictions of RCS Comparison of RCS Predictions

Distribution Statement (Continued)

. Abstract (Continued)

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UNCLASSIFIED Security Classification

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